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Finding the Third Proportional to 6,497 and 14,305

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Solution

The third proportional to 6,497 and 14,305 is: 31,496.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,497 : 14,305 = 14,305 : x
  2. Step 2: Convert to fraction form
    6,497/14,305 = 14,305/x
  3. Step 3: Cross multiply
    6,497x = 14,305 × 14,305
  4. Step 4: Simplify right side
    6,497x = 204,633,025
  5. Step 5: Solve for x
    x = 204,633,025/6,497
  6. Step 6: Final answer
    x = 31,496.54

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.